The President nominates someone for a vacancy on the Court and the Senate votes to confirm the nominee, which requires a simple majority. In this way, both the Executive and Legislative Branches of the federal government have a voice in the composition of the Supreme Court.

The Constitution does not specify qualifications for Justices such as age, education, profession, or native-born citizenship. A Justice does not have to be a lawyer or a law school graduate, but all Justices have been trained in the law. Many of the 18th and 19th century Justices studied law under a mentor because there were few law schools in the country.

• The last Justice to be appointed who did not attend any law school was James F. Byrnes (1941-1942). He did not graduate from high school and taught himself law, passing the bar at the age of 23.
• Robert H. Jackson (1941-1954). While Jackson did not attend an undergraduate college, he did study law at Albany Law School in New York. At the time of his graduation, Jackson was only twenty years old and one of the requirements for a law degree was that students must be twenty-one years old. Thus rather than a law degree, Jackson was awarded with a "diploma of graduation." Twenty-nine years later, Albany Law School belatedly presented Jackson with a law degree noting his original graduating class of 1912.

Like the Associate Justices, the Chief Justice is appointed by the President and confirmed by the Senate. There is no requirement that the Chief Justice serve as an Associate Justice, but 5 of the 17 Chief Justices have served on the Court as Associate Justices prior to becoming Chief Justice.

Three were members of the Court when they were elevated to Chief Justice:

• Edward Douglas White (Associate Justice 1894-1910, Chief Justice 1910-1921)
• Harlan Fiske Stone (Associate Justice 1925-1941, Chief Justice 1941-1946)
• William H. Rehnquist (Associate Justice 1972-1986, Chief Justice 1986-2005)

Two had a break in service between their periods of service:

• John Rutledge (Associate Justice 1789-1791, Chief Justice 1795)
• Charles Evans Hughes (Associate Justice 1910-1916, Chief Justice 1930-1941)

The Constitution states that Justices "shall hold their Offices during good Behaviour." This means that the Justices hold office as long as they choose and can only be removed from office by impeachment.

The only Justice to be impeached was Associate Justice Samuel Chase in 1805. The House of Representatives passed Articles of Impeachment against him; however, he was acquitted by the Senate.

The Constitution places the power to determine the number of Justices in the hands of Congress. The first Judiciary Act, passed in 1789, set the number of Justices at six, one Chief Justice and five Associates. Over the years Congress has passed various acts to change this number, fluctuating from a low of five to a high of ten. The Judiciary Act of 1869 fixed the number of Justices at nine and no subsequent change to the number of Justices has occurred.

The federal circuit courts of appeals and district courts are organized into 13 federal circuits and each Justice is responsible for emergency applications and other matters from one or more of these circuits. For example, individual Justices may be asked to halt the implementation of a circuit court order, set bond for a defendant, or stop the deportation of an alien. Justices are also asked to act on applications for a stay of execution.

A quorum of six Justices is required to decide a case. Justices may also participate in a case by listening to audio recordings of the oral arguments and reading the transcripts.

The Court receives approximately 7,000-8,000 petitions for a writ of certiorari each Term.  The Court grants and hears oral argument in about 80 cases.

The first meeting of the Court was scheduled to take place in New York City on Monday, February 1, 1790, but the lack of a quorum (only three of the six Justices were present) delayed the official opening until the following day, Tuesday, February 2, 1790.

As stipulated by the Judiciary Act of 1789, there was one Chief Justice, John Jay, and five Associate Justices: James Wilson, William Cushing, John Blair, John Rutledge and James Iredell. Only Jay, Wilson, Cushing, and Blair were present at the Court's first sitting.

The Court met in New York City at the Exchange Building (also known as the Royal Exchange, or the Merchants’ Exchange).

From 1791-1800, the Court met in Philadelphia, twice in the Pennsylvania State House (Independence Hall) and later in the City Hall (known today as Old City Hall).

From February 1801 to the present, the Court has met in the city of Washington. After using several temporary locations in the U.S. Capitol, the Court settled into a courtroom on the ground floor of the North Wing where it met from 1810 to 1860 (excluding the years the courtroom was repaired after the British burned the Capitol in 1814). Today this room is known as the Old Supreme Court Chamber. From 1860 to 1935, the Court met in what is known today as the Old Senate Chamber.

The Supreme Court sat for the first time in its own building on October 7, 1935. It had opened for visitors during the summer of 1935. Charles Evans Hughes was Chief Justice.

Cass Gilbert. Among his other famous buildings are the Woolworth Building in New York City, the Minnesota State Capitol, and the West Virginia State Capitol. Two other architects, John Rockart and Cass Gilbert, Jr., were listed on the contract and were involved with the project, especially after Cass Gilbert, Sr., died in 1934.